A large part of maintaining the positive environment at the Shabbos table is ensuring that the content of discussion is of the correct ilk. Given the fact that the whole family is together / hosting other people at the meal, it represents a good opportunity to enjoy "שיחות משותפות" – “mutual conversation”.1 A time to give attention to everyone and engage in reciprocal dialogue.
I have found the following approaches help:
1) Ask a question / moral dilemma to the table
A good tactic is to ask an opening question that provides room for interaction and an ensuing table discussion. As the viewpoints are increasingly shared everyone becomes more invested in the dialogue and wants to see what the conclusion is. Halachic dilemmas posed by Rav Zilberstein shlita in his series of books for example, make for a fascinating table discussion.2
2) Tell a story
Everyone loves a good story. Not only do they often keep people engaged, they serve as a wonderful form of mussar or chizuk.
This too is a wonderful tool for chinuch. The Slonimer Rebbe in his Nesivei Chinuch, Chapt 7, p.52 relates:
עלינו להשתמש גם בסיפורי צדיקים מילדותם, ובמיוחד בש"ק בעת הסעודה, שעי"ז תתפתח השאיפה בלב ובנפש הבנים לילך ג"כ ברוח זו, וירגישו כי שקר החן והבל היופי של מצות אנשים מלומדה והחכמות אשר בחוץ תרונה, וישאפו לנקודת אמת ותתעורר בהם אש קודש
We should specifically relate stories about tzaddikim in their youth at the Shabbos meal. In so doing, it cultivates an aspiration in both the heart and soul of our children to try to replicate their actions. They will also feel that there is a sense of falsehood and shallowness in mitzvah observance that one gleans from an external commitment and it will inspire in them the point of truth and awaken in them a holy fire.
Providing the tone remains light-hearted and each question is age-appropriate, these question-answer sessions can become a real highlight of the meal. Obviously it should not be a pressure, but a fun way to engage in Torah during the meal.It does not necessarily need to be parsha-based trivia but even yedios klalis (Jewish general knowledge), it can become a very informative and entertaining part of the meal. One should definitely ensure that a number of questions will warrant correct answers as that breeds confidence and makes the experience more enjoyable.
4) A thought based off a nicely sung zemer
The custom of singing zemiros is something that is praised in the Gemara3, and is regarded as a clear expression of love for Hashem. As such, zemiros are a chance to collectively sing together enjoying all sorts of familiar tunes. It is a nice way to break up the meal so that the mealtime scenario does not become too monotonous and instead further enhances the Shabbos meal. I have found that sometime a nicely sung zemer can be used as a good segue into bringing out an idea as those who enjoy singing feel a connection to the song and are resultantly more attentive.
1 A term borrowed from Rabbi Yoel Schwartz in his sefer on Chinuch - Beis Abbah, p.93 (last paragraph on the page).
2 See either his והערב נא series of halachic challenges and solutions based on the weekly parsha (Vol.1, Vol.2, Vol.3, Vol. 4) and their English translation by Feldheim (Vol.1, Vol.2, Vol.3), as well as the What If set produced by Artscroll based off his חשוקי חמד series (Vol.1, Vol.2, Vol.3, Vol.4, Vol.5). Another good option is Rabbi Michoel Fletcher’s series of Do you know… book produced by Menucha Publishers. For example in his Do you know Hilchos Shabbos, he presents a number of everyday questions based round the 39 מלאכות which can be asked to the family to decide what the halachic outcome is, before seeing his answers.
3 Refer to Megilla 12b where Rava explains the difference between how Jews and the non-Jews enjoy their meals, with one of the differences being that the Jews partake of "דברי תשבחות" – “Words of praise (to Hashem)”. Also see Tosafos s.v. מכנף הארץ זמירות שמענו in Sanhedrin 37b which notes how the custom in Eretz Yisroel was to recite the kedusha only on Shabbos. The reason being because the angels have six wings corresponding to the six days of the week singing and the seventh day – שבת is reserved for the Jewish people to engage in singing זמירות.